This invention relates to a fossil-fired boiler, and, more particularly, to a method for determining its thermal efficiency to a high accuracy from its basic operating parameters.
This application is related to U.S. Pat. Nos. 5,367,470 and 5,790,420 which patents are incorporated herein by reference in their entirely. Performance Test Codes 4.1 and 4 published by the American Society of Mechanical Engineers (ASME) are incorporated herein by reference in their entirely.
The importance of accurately determining boiler efficiency is critical to any thermal system which heats a fluid by combustion of a fossil fuel. If practical day-to-day improvements in thermal efficiency are to be made, and/or problems in thermally degraded equipment are to be found and corrected, then accuracy in efficiency is a necessity.
The importance of accurately determining boiler efficiency is also critical to the Input/Loss Method. The Input/Loss Method is a patented process which allows for complete thermal understanding of a steam generator through explicit determinations of fuel and effluent flows, fuel chemistry including ash, fuel heating value and thermal efficiency. Fuel and effluent flows are not directly measured. The Method is designed for on-line monitoring, and hence continuous improvement of system heat rate.
The tracking of the efficiency of any thermal system, from a classical industrial view-point, lies in measuring its useful thermal output, BBTC, and the inflow of fuel energy, mAF(HHVP+HBC). mAF is the mass flow of fuel, HHVP is the fuel""s heating value, and HBC is the Firing Correction term. For example, the useful output from a fossil-fired steam generator is its production of steam energy flow. Boiler efficiency (xcex7B-HHV) is given by: xcex7B-HHV=BBTC/[mAF(HHVP+HBC)]. The measuring of the useful output of thermal systems is highly developed and involves the direct determination of useful thermal energy flow. Determining thermal energy flow generally involves measurement of the inlet and outlet pressures, temperatures and/or qualities of the fluids being heated, as well as measurement of the fluid""s mass flow rates (mstm). From this information specific enthalpies (h) may be determined, and thus the total thermal energy flow, BBTC=xcexa3mstm(houtletxe2x88x92hinlet), delivered from the combustion gases may be determined.
However, when evaluating the total inflow of fuel energy, problems frequently arise when measuring the flow rate (mAF) of a bulk fuel such as coal. Further, the energy content of coal, its heating value (HHV), is often not known with sufficient accuracy. When such difficulties arise, it is common practice to evaluate boiler efficiency based on thermal losses per unit mass flow of As-Fired fuel (i.e., Btu/lbmAF); where: xcex7B-HHV=1.0xe2x88x92(xcexa3Losses/mAF)/(HHVP+HBC). For evaluating the individual terms comprising boiler efficiency, such as the specific loss term (xcexa3Losses/mAF), there are available numerous methods developed over the past 100 years. One of the most encompassing is offered by the American Society of Mechanical Engineers (ASME), published in their Performance Test Codes (PTC).
This invention teaches the determination of boiler efficiency having enhanced accuracy. Boiler efficiency, if thermodynamically accurate, will guarantee consistent system mass/energy balances. From such consistencies, fuel flow and effluent flow then may be determined, having greater accuracy than prior art, and greater accuracy than obtained from direct measurements of these flows.
Before discussing details of the present invention it is useful to examine ASME""s PTC 4.1, Steam Generating Units, and PTC 4, Fired Steam Generators. Both PTC study a boiler efficiency based on the higher heating value (xcex7B-HHV), no mention is made of a lower heating value based efficiency (xcex7B-LHV). Using PTC 4.1""s Heat-Loss Method, higher heating value efficiency is defined by the following. For Eq. (1A), HHV, if determined from a constant volume bomb calorimeter, is corrected for a constant pressure process, termed HHVP. Gaseous fuel heating values, normally determined assuming a constant pressure process, need no such correction, HHVP=HHV.                               η                      B            -            HHV                          =                              HHVP            +            HBC            -                          ∑                              Losses                /                                  m                  AF                                                                          HHVP            +            HBC                                              (1A)            
Using PTC 4""s Heat-Balance Method, higher heating value efficiency is defined as:                               η                      B            -                          HHV              /              fuel                                      =                              HHVP            -                          ∑                              Losses                /                                  m                  AF                                                              HHVP                                    (1B)            
The above are considered indirect means of determining boiler efficiency. Eq. (1A) implies that the input energy in fuel and Firing Correction mAF(HHVP+HBC) less xcexa3Losses, describes the xe2x80x9cEnergy Flow Deliveredxe2x80x9d from the thermal system, the term BBTC. The newer PTC 4 (1998, but first released in 2000) advocates only the use of heating value in the denominator, developing a so-called xe2x80x9cfuelxe2x80x9d efficiency, xcex7B-HHV/fuel. It is important to recognize that once efficiency is determined using an indirect means, fuel flow may be back-calculated using the classic definition provided BBTC is determinable: mAF=BBTC/[xcex7B-HHV(HHVP+HBC)]; or mAF=BBTC/[xcex7B-HHV/fuelHHVP].
The concept of the Enthalpies of Products and Reactants is now introduced as important to this invention. These terms both define heating value and justify the Firing Correction term (HBC) as being intrinsically required in Eq. (1A) Higher heating value is the amount of energy released given complete, or xe2x80x9cidealxe2x80x9d, combustion at a defined xe2x80x9ccalorimetric temperaturexe2x80x9d. For a solid fuel such as coal, evaluated in a constant volume bomb, the combustion process typically heats a water jacket about, and is corrected to, the calorimetric temperature. Any such ideal combustion process is the difference between the enthalpy of ideal products (HPRIdeal) less reactants (HRXCal) both evaluated at the calorimetric temperature, TCal. Correction from a constant volume process (HHV) associated with a bomb calorimeter, if applicable, to a constant pressure process (HHVP) associated with the As-Fired condition is made with the xcex94HV/P term, see Eq. (37B).
xcex4QT-Cal=xe2x88x92HHV=xe2x88x92HHVP+xcex94HV/Pxe2x80x83xe2x80x83(2A)
HHVPxe2x89xa1=xe2x88x92HPRIdeal+HRXCalxe2x80x83xe2x80x83(2B)
This invention teaches that only when fuel is actually fired at exactly TCal, and whose combustion products are cooled to exactly TCal, is the thermodynamic definition of heating value strictly conserved. At any other firing and cooling temperatures, Firing Correction and sensible heat losses must be applied. At any other temperature the so-called xe2x80x9cfuelxe2x80x9d efficiency (which ignores the HBC correction), is thermodynamically inconsistent. At any other temperature, evaluation of the HRXCal term must be corrected to the actual As-Fired condition through a Firing Correction referenced to TCal. The HPRIdeal term is corrected to the actual via loss terms referenced to TCal where appropriate (that is, anywhere a xcex94energy term is applicable).
When a fossil fuel is fired at a temperature other than TCal, the Firing Correction term HBC must be added to each side of Eq. (2B):
HHVP+HBC=xe2x88x92HPRIdeal+HRXCal+HBCxe2x80x83xe2x80x83(3A)
Eq. (3A) implies that for any As-Fired condition, the systems"" thermal efficiency is unity, provided the HPRIdeal term is conserved (i.e., system losses are zero, and ideal products being produced at TCal). For an actual combustion process, the HPRIdeal term of Eq. (3A) is then corrected for system losses, forming the basis of boiler efficiency:
xcex7B-HHV(HHVP+HBC)=xe2x88x92HPRIdealxe2x88x92xcexa3Losses/mAF+HRXCal+HBCxe2x80x83xe2x80x83(3B)
This invention recognizes that the HPRIdeal term of Eqs. (2B) and (3A), and thus Eq. (3B), is key in accurately computing boiler efficiency stemming from Eq. (3B). This invention teaches that all terms comprising Eq. (3B) must be evaluated with methodology consistent with a boiler""s energy flows, but also, and most importantly, in such a manner as to not impair the numerical consistency of the HPRIdeal term as referenced to TCal.
The approaches contained in prior art have not appreciated using the concept of TCal, used for thermodynamic reference of energy levels as affecting the major terms comprising boiler efficiency. It is believed that prior approaches evaluated fuel heating value, and especially that of coal, only to classify fuels. Boiler efficiencies were determined as relative quantities. Accuracy in heating value, and in the resultant computed fuel flow, was not required but only accuracy in the total system fuel inflow of energy was desired. The accuracy needed in boiler efficiency by the Input/Loss Method, given that fuel chemistry, fuel heating value and fuel flow are all computed, requires the method of this invention. Further, commercial needs for high accuracy boiler efficiency was not required until recent deregulation of the electric power industry which has now necessitated improved accuracy.
The sign convention associated with the HPR and HRX terms of Eq. (2B) follows the assumed convention of a positive numerical heating value, thus the non-conventional sense of HPR and HRX. In some technical literature the senses of HPR and HRX terms may be found reversed for simplicity of presentation. An example of typical values includes: [xe2x88x92HPRAct-HHV+HRXAct-HHV]=xe2x88x92(xe2x88x927664)+(xe2x88x921064), Btu/lbm. The sign of sensible heat terms, ∫dh, follows this difference:xe2x88x92HPRActxe2x88x92∫dhProducts; and +HRXAct+∫dhReactants. Heats of Formation, xcex94Hf0, are always negative quantities. From Eq. (3B), higher heating value boiler efficiency is then given by:                               η                      B            -            HHV                          =                                            -                              HPR                Ideal                                      -                          ∑                              Losses                /                                  m                  AF                                                      +                          HRX              Cal                        +            HBC                                HHVP            +            HBC                                              (3C)            
For certain fuels the PTC procedures are flawed by not recognizing the calorimetric temperature, TCal, and its impact on the HPRIdeal term. As discussed below, for certain coals having high fuel water, and for gaseous fuels, use of the calorimetric temperature becomes mandated if using the methods of this invention for accurate boiler efficiencies; without such consideration, errors will occur. There is no mention of the calorimetric temperature in PTC 4.1 nor in PTC 4. PTC 4.1 references energy flows to an arbitrary xe2x80x9creference air temperaturexe2x80x9d, TRA. PTC 4 references energy flows to a constant 77.0F. PTC 4.1 nor 4 mention how the reference temperature should be evaluated. U.S. Pat. No. 5,790,420 (bottom of col.18) also assumes a constant reference temperature at 77.0F, without mention of a variable calorimetric temperature, nor how the reference temperature should be evaluated. There is no mention of a calorimetric temperature as used in boiler efficiency calculations in the technical literature. Further, the PTC 4 procedure is flawed by recommending a so-called xe2x80x9cfuelxe2x80x9d efficiency, which, again, is in disagreement with the base definition of heating value if the fuel is actually fired (As-Fired) at a temperature other than TCal. For some high energy coals the effects of ignoring TCal have minor impact. However, when using coals having high water contents (e.g., lignites commonly found in eastern Europe and Asia), and for gaseous fuels, such effects may become very important.
To illustrate, consider a simple system firing pure carbon in dry air, having losses only of dry gas, effluent CO and unburned carbon. Assume Forced Draft (FD) and Induced Draft (ID) fans are used having WFD and WID energy flows. Applying PTC 4.1 xc2xa77.3.2.02, but using nomenclature herein, dry gas loss is evaluated at the reference air temperature, thus LGxe2x80x2 in Btu/lbmAF is given by:
LGxe2x80x2=CP/Gas(TStackxe2x88x92TRA)Mxe2x80x2Gasxe2x80x83xe2x80x83(4)
Incomplete combustion is described (xc2xa77.3.2.07) as the fraction of CO produced relative to total possible effluent CO2 times the difference in Heats of Combustion of carbon and CO.
LCO=(xe2x88x92xcex94Hf-Cal/CO20+xcex94Hf-Cal/CO0)Mxe2x80x2COxe2x80x83xe2x80x83(5)
Unburned carbon is described in PTC 4.1 xc2xa77.3.2.07, as the flow of refuse carbon times its Heat of Combustion:
LUC=(xe2x88x92xcex94Hf-Cal/CO20)Mxe2x80x2C/Flyxe2x80x83xe2x80x83(6)
For this simple example, and assuming unity fuel flow, the so-called xe2x80x9cboiler creditsxe2x80x9d as defined, in part, by PTC 4.1 are determined as:
HBCxe2x80x2=CP/Fuel(TFuelxe2x88x92TRA)+CP/Air(TAmbxe2x88x92TRA)Mxe2x80x2Air+WFDxe2x80x83xe2x80x83(7)
In these equations the Mxe2x80x2i weight fractions are relative to As-Fired fuel, and have direct translation to 4.1 usage. PTC 4.1 efficiency is then given by the following, after combining the above quantities into Eq. (3C), and re-arranging terms:                               η          B                =                                                                                                  -                                          HPR                      Ideal                                                        -                                                                                    C                                                  P                          /                          Gas                                                                    ⁡                                              (                                                                              T                            Stack                                                    -                                                      T                            RA                                                                          )                                                              ⁢                                          M                      Gas                      xe2x80x2                                                        -                                      W                    ID                                    -                                                                                                                                                (                                                                                                    -                            Δ                                                    ⁢                                                      xe2x80x83                                                    ⁢                                                      H                                                          f                              -                                                              Cal                                /                                CO2                                                                                      0                                                                          +                                                  Δ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      H                                                          f                              -                                                              Cal                                /                                CO                                                                                      0                                                                                              )                                        ⁢                                          M                      CO                      xe2x80x2                                                        -                                                                                                                                                (                                                                        -                          Δ                                                ⁢                                                  xe2x80x83                                                ⁢                                                  H                                                      f                            -                                                          Cal                              /                              CO2                                                                                0                                                                    )                                        ⁢                                          M                                              C                        /                        Fly                                            xe2x80x2                                                        +                                      HRX                    Cal                                    +                                                            C                                              P                        /                        Fuel                                                              ⁡                                          (                                                                        T                          Fuel                                                -                                                  T                          RA                                                                    )                                                        +                                                                                                                                                                        C                                                  P                          /                          Air                                                                    ⁡                                              (                                                                              T                            Amb                                                    -                                                      T                            RA                                                                          )                                                              ⁢                                          M                      Air                      xe2x80x2                                                        +                                      W                    FD                                                                                            HHVP            +            HBC                                              (        8        )            
The present invention is a complete departure from all known approaches in determining boiler efficiency, including PTC 4.1 and PTC 4. Eq. (8) illustrates the generic approach followed by PTC 4.1 and PTC 4, which has been used by the power industry for many years. However, this invention recognizes and corrects several discrepancies which affect accuracy. These discrepancies include the following items.
1) The enthalpy terms HPRIdeal and HRXCal as referenced to the calibration temperature, when xe2x80x9ccorrectedxe2x80x9d to system boundary conditions using (TStackxe2x88x92TRA) and (TFuelxe2x88x92TRA) is wrong since TRAxe2x89xa0TCal. Although the effects on HPRIdeal from HBC referenced to TRA, may cancel; the effects on HPRIdeal from the xcexa3Losses/mAF term, as referenced to TRA, does not cancel. See PTC 4.1 xc2xa77.2.8.3 and xc2xa77.3.2.02.
2) PTC 4.1 addresses unburned fuel and incomplete combustion through Heats of Combustion. Although numerically correct as referenced to HPRIdeal, a more logical approach is to describe actual productsxe2x80x94their effluent concentrations and specific Heats of Formation, xcex94Hf-Cal0. For example, although the above Mxe2x80x2Gas. is descriptive of actual combustion products, differences between actual and ideal demand numerical consistency with HHVP, product formations and associated heat capacities. See PTC 4.1 xc2xa77.3.2.01, xe2x88x9207.
3) Uncertainty is present when using Heats of Combustion associated with unburned fuel. As coal pyrolysis creates numerous chemical forms (the breakage of aliphatic Cxe2x80x94C bonds, elimination of heterocycle complexes, the hydrogenation of phenols to aromatics, etc.), the assumption of an encompassing xcex94HC0 used by PTC 4.1 is optimistic. For example, various graphites have a wide variety of xcex94HC0 values (from 13,970 to 14,540 Btu/lb depending on manufacturing processes). An improved approach is use of consistent Heats of Formation coupled with measured effluent gas concentrations and balanced stoichiometrics.
4) HHVP reflects formation of ideal combustion products at TCal; water thus formed must be referenced to xcex94Hf-Cal/liq0 and hf-Cal (not illustrated above). For example, if using TRA as reference, water""s xcex94Hf/liq0 varies from xe2x88x926836.85 Btu/lbm at 40F to xe2x88x926811.48 Btu/lbm at 100F, hf from 8.02 to 68.05 Btu/lbm. Holding these terms constant is suggested by PTC 4.1 xc2xa77.3.2.04.
5) PTC 4.1 xc2xa77.3.2.13 pulverizer rejected fuel losses are described by the rejects weight fraction times rejects heating value, HHVRej (not illustrated above). This is correct only if the heating value is the same as the As-Fired. If mineral matter is concentrated in the rejects (reflected by a HHVRej term), then fuel chemistry (and HPR and HRX terms) must be adjusted, again, to conserve HPRIdeal for the As-Fired.
Of course, one could equate TRA to TCal (not suggested by PTC 4.1 or 4), and solve some of the problems. However, the rearrangement of individual terms of Eq. (8) and then, most importantly, their combinations into HPRAct, HRXAct and HBC terms evaluated at TCal, provides the nucleus for this invention. These methods are not employed by any known procedure. First, the issue of possible inconsistency between ideal arid actual products is addressed by simplifying (for the example cited) the entire numerator of Eq. (8) to [xe2x88x92HPRAct+HRXAct]. In this, the Enthalpy of Products, HPRAct, encompasses effluent sensible heat and xcex94Hf-Cal0 terms associated with actual products, including all terms associated with incomplete combustion. The Enthalpy of Reactants, HRXAct, is defined as [HRXCal+HBC], the last line of Eq. (8); HRXCal is evaluated as [HHVP+HPRIdeal] from Eq. (2B). Second, use of the [xe2x88x92HPRAct+HRXAct] concept allows ready introduction of the calorimetric temperature (or any reference temperature if applicable) as affecting both ∫dh and xcex94Hf-Cal0 terms. Third, the [xe2x88x92HPRAct+HRXAct] concept provides generic methodology for any combustion situation. It is believed the elimination of individual loss terms associated with combustion (cornionly used by the industry and as practiced in PTC 4.1 and PTC 4) greatly reduces error in determining total stack losses, including the significant dry stack gas loss term as will be seen; [xe2x88x92HPRAct+HRXAct]=HHVP+HBCxe2x88x92xcexa3(Stack Losses)/mAF.
The use of the term xe2x80x9cboiler creditxe2x80x9d (for HBCxe2x80x2) as used by the PTCs is misleading since terms comprising HBC intrinsically correct the fuel""s calorimetric energy base to As-Fired conditions. HBC is herein termed the xe2x80x9cFiring Correctionxe2x80x9d. HBC is not a convenience nor arbitrary, it is required for HHVP consistency and thus valid boiler efficiencies leading to consistent mass and energy balances.
Although the basic philosophies of PTC 4.1 and 4 are useful and have been employed throughout the power industry, including prior Input/Loss Methods, they are not thermodynamically consistent. To address these issues this invention includes establishing an ordered approach to boiler efficiency calculations employing a strict definition of heating value, that is, consistent treatment of the Enthalpy of Products, the Enthaply of Reactants and the Firing Correction such that the numerical evaluation of the HPRIdeal term is conserved.
This invention teaches the determination of lower heating value based boiler efficiency (commonly used in Europe, Asia, South America and Africa), such that fuel flow rate is computed the same from either a lower or a higher heating value based efficiency.
Other advantages of this invention will become apparent when the details of the method of the present invention is considered.
This invention teaches the consistent application of the calorimetric temperature to the major terms comprising determination of boiler efficiency. The preferred method of the application of such a temperature is through the explicit calculation of these major terms, which include the Enthalpy of Products, HPRAct, the Enthalpy of Reactants, HRXAct, and the enthalpy of Firing Correction, HBC. This method advocates an ordered and systematic approach to the determination of boiler efficiency. For some fuels, under certain conditions, techniques of this invention may be applied using an arbitrary reference temperature.